System and method for spatial multiplexing in LoS environments

ABSTRACT

The present system and method provides a spatial multiplexing scenario that is performed purely in the analog domain when transmit and receive arrays are in Line of Sight (LoS) and hence significantly reduce the DSP requirements of massive MIMO systems.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/159,844, filed Oct. 15, 2018, which application is a continuation ofU.S. application Ser. No. 15/856,557, filed Dec. 28, 2017, whichapplication is a divisional of U.S. application Ser. No. 14/937,292,filed Nov. 10, 2015, the disclosures and benefits of which are herebyincorporated in their entireties by reference herein.

BACKGROUND

In wireless communications, MIMO processing is typically done atbaseband and in the digital domain. FIG. 1 illustratively representssuch a prior art system 10. Transmit symbols 10 are passed through abaseband digital MIMO processor 20 before transmission. MIMO processor20 is configured with a pre-processor/pre-coder. Processor 20 utilizes,for example, a pre-coding matrix, which determines the number of spatialstreams, the spatial multiplexing, and beamforming gains. System 10 alsoincludes an antenna array for transmitting the digitally processed data.In large-scale antenna systems (e.g., massive MIMO in 5G wirelesssystems), the digital processing can be significantly high, which addscost, complexity, increased point of failure, energy consumption, etc.

SUMMARY OF THE INVENTION

The present spatial multiplexing system and method is performed purelyin the analog domain between transmit and receive arrays that are withinline of sight (LoS) of one other. Such a system and method significantlyreduces the digital signal processing (DSP) requirements for massiveMIMO systems. Examples of systems that may benefit from these novelareas include 5G and massive MIMO systems,

A present disclosure describes a system and method for analog, line ofsight (LoS) spatial multiplexing communication, which recovers one ormore of analog transmit signals from two or more of analog receivesignals. The present system and method accomplishes this by processingtwo or more analog receive signals within a receive processor byapplying at least a portion of an inverse steering matrix to a pluralityof analog receive signals (also discussed as a receive vector) receivedat a receive array. By applying the inverse steering matrix to aplurality of analog receive signals the system and method can extractone or more analog transmit signals from the inverse steering matrixprocessed two or more analog receive signals.

In an embodiment, the present system and method is configured to converttwo or more transmit modulation symbols into the two or more analogtransmits signals and transmit the analog transmit signals from two ormore different transmit antenna elements of a transmit array and receivetwo or more analog receive signals at two or more receive antennaelements of a receive array. The two or more analog receive signals aredifferent combinations of the transmitted signals.

In an embodiment, the present system and method utilizes a first andsecond transmit element and a first receive element. A separationdistance, D, between the first and second transmit element is such thatsignals sent from the first and second transmit element that arereceived at the first receive element are out of phase by apredetermined amount to facilitate analog processing at the receive sideto cover the transmitted signals.

In an embodiment, the present system and method utilizes a relationshipbetween transmit and receive signals as described by an inverse steeringmatrix to recover a transmit vector from a receive vector.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 schematically illustrates a prior art digital MIMO processingsystem.

FIG. 2 schematically representation a spatial multiplexing system withLoS propagations, in an embodiment.

FIG. 3A schematically representation of an analog spatial multiplexingprocessing system with LoS propagation, in an embodiment.

FIG. 3B schematically representation of an n=3 receive analog processor,in an embodiment.

FIG. 4 shows the analog processing spatial multiplexing system with LoSpropagation of FIG. 3A with n=2, in an embodiment.

FIG. 5 is a flow chart for implementing analog, spatial multiplexingcommunication, in an embodiment.

DETAILED DESCRIPTION OF THE FIGURES

Massive MIMO is one of the key technologies for 5G communication systemsand is particularly amenable in millimeter wave (mmWave) communicationsystems. Recent work in massive MIMO has focused on hybrid beamformingtechniques. Hybrid Beamforming is a combination of analog and digitalBeamforming and results in a tradeoff between hardware complexity andsystem performance.

In mmWave communication systems, the channel tends to be Ricean due tothe use of large antenna arrays, which can filter most multipathsignals. Furthermore, in a small cell, which is one of the keytechnologies utilized in 5G systems, LoS propagation is more likely tooccur. The present disclosure details a spatial multiplexing techniqueperformed purely in the analog domain and between LoS transmit andreceive arrays.

Problem Formulation

One embodiment of the present system is implemented as a uniform lineararray (ULA) of transmit and receive antenna elements, each with nantenna elements. One aspect of the present system and method determinesa minimum distance between antenna elements (e.g., transmit antennaelements), D_(ULA). Minimum distance D_(ULA) enables a preferredseparation of, for example, transmitted signals received at anassociated receiving system and is calculated as,

$\begin{matrix}{{D_{ULA} = \sqrt{\frac{R\;\lambda}{n}}},} & (1)\end{matrix}$where ‘R’ represents the distance between transmit and receive arrays,λ is the transmit wavelength, andn is the number of antenna elements in the transmit array.

It will be understood that in a uniform planar array (UPA) having n×ntransmit and receive arrays, the minimum distance will be the similar tothe ULA case, i.e.,

$D_{UPA} = {\sqrt{\frac{R\;\lambda}{n}}.}$In addition, a uniform planar array (UPA) may have n×m transmit andreceive arrays, or n×m transmit arrays and j×k receive arrays withoutdeparting form the scope herein. For these reasons, and for purposes ofclarity, all examples and embodiments are discussed in a ULA system orare described generically. It will be understood that the systems andmethods described below also apply to uniform planar arrays and mayrequire only trivial modification, if any at all for use with uniformplanar arrays. In addition, for sake of clarity D_(UPA) and D_(ULA) aresometimes replaced by the generic distance variable ‘D’, which denotesthe minimum separation distance between the antenna elements in an arrayto enable a preferred separation of transmitted signals at an associatedreceiving system.

FIG. 2 shows an analog, spatial multiplexing system 200 with LoSpropagations. System 200 is shown with transmit analog processor 260,transmit array 202, receive analog processor 262, and receive array 204.Transmit array 202 is formed with n transmit elements 202(1)-202(n).Receive array 204 is formed with n receive elements 204(1)-204(n).System 200 is shown with two signals 250 and 252. Signal 250 originatesat transmit element 202(i) and terminates at receive element 204(i).Signal 252 originates at transmit element 202(i+1) and terminates at thesame the same receive element 204(i). Signal 250 has a path length R 210and signal 214 has a path length √{square root over (D²+R²)} 214. Pathlength R 210 is equivalent to the separation distance between transmitarray 202 and receive array 204. Signal 252's path length √{square rootover (D²+R²)} 214 may be calculated as,

$\begin{matrix}{\sqrt{D^{2} + R^{2}} = {\sqrt{\frac{R\;\lambda}{n} + R^{2}} = {{{R\sqrt{1 + \frac{\lambda}{nR}}} \approx {R\left( {1 + \frac{\lambda}{2{nR}}} \right)}} = {R + {\frac{\lambda}{2n}.}}}}} & (2)\end{matrix}$It should be understood that transmit and receive arrays need not havethe same number of transmit and receive elements. That is, a transmitarray may be configured with n transmit elements and a receive array maybe configured with m receive elements, where n≠m. If n≠m the equationsdiscussed below will require modification, although such changes arewell within the capabilities of the skilled artisan.

The difference between path lengths R and

$R + \frac{\lambda}{2n}$can cause a phase difference between signals 250 and 252. For example,in system 200 with 2π radians within a single wave length), there may beas much as

$\varphi = {\frac{2\pi}{2n} = \frac{\pi}{n}}$phase difference between signals 250 and 252. Furthermore, there may beas much as

$\varphi = \frac{k\;\pi}{n}$phase difference between signal 250 and a signal transmitted fromtransmit antenna elements 202(i+k) (not shown to maintain clarity ofillustration) and received by the same receive element 204(i). Thus thephase difference between signals 250 and 252 is

$\varphi = \frac{k\;\pi}{n}$which is merely the case where k=1. It will be understood by the skilledartisan that a similar issue exists in UPA system (not shown).

It should also be understood that the difference between path lengthscan cause a phase difference between signals transmitted by the sametransmit element and received by different receive elements, for examplesignals 252 and 253 transmitted by element 202(i+1) and received byelements 204(i) and 204(i+1). Similar to that discussed above, in system200 there may be as much as

$\varphi = \frac{\pi}{n}$phase difference between signals 252 and 253.

FIG. 3A depicts one embodiment of an analog spatial multiplexing systemwith LoS propagation, system 300, represented in block diagram. System300 is similar to LoS system 200, FIG. 2 but additionally shows areceive analog processor 362, which is similar to receive analogprocessor 262 of FIG. 2, including inverse steering matrix componentsZ₁₁-Z_(1n) 324 and summation block Σ₁-Σ_(n) for recovering signalX₁-X_(n). System 300 is shown with a transmit analog processor 360transmitting a vector X 312 of X₁-X_(n) transmit symbols 312(1)-312(n)from a transmit array 302 and a receive analog processor 362 connectedto a receive array 304 for receiving a vector Y 314 of Y₁-Y_(n) receivedata 314(1)-314(n). Shown connected to each receive element304(1)-304(n) is one of the inverse steering matrix componentsZ₁₁-Z_(1n) 324, respectively. The Z₁₁-Z_(1n) function blocks form aninverse steering matrix array, which represent the Z₁₁-Z_(1n) entries ininverse steering matrix Z, discussed in more detail below. Transmitarray 302 and received array 304 are similar to transmit array 202 andreceive antenna 204, respectively. Transmit analog processor 360 andreceive analog processor 362 are similar to transmit analog processor260 and receive analog processor 262, respectively. Inverse steeringmatrix function blocks Z₁₁-Z_(1n) apply the i^(th) inverse steeringmatrix Z element to the respective i^(th) receive signal in the vectorof received signals Y. For sake of clarity of illustration only inversesteering matrix components Z₁₁-Z_(1n) 324 connected to summation blockΣ₁ 322(1) for recovering transmit signal X₁ are shown. Additional setsof inverse steering matrix components 324 may be provided for recoveringone or more other transmit signals 312 X₂-X_(n). Alternatively, theexisting inverse steering matrix components 324 represent a singlecomponent or a set of components that may be adapted, configured,programmed, etc. to apply an appropriate inverse steering functionextracted from an appropriate entry Z₁₁-Z_(nn) in the inverse steeringmatrix (see equation (5), below) to the received signals Y₁-Y_(n) 314for purposes of recovering one or more of transmit signals X₁-X_(n) 312.

One exemplary receive analog processor 362B is symbolically representedin FIG. 3B. Receive control 362B is configured with inverse steeringmatrix components 324B, and summation blocks 322(1)-(3) which outputrecovered transmit signals X₁-X₃ 312(1)-(3). Inverse steering matrixcomponents 324B is in communication with receive array 304 and summationblocks 322.

Receive signal Y₁ is sent to the Z₁₁, Z₂₁, and Z₃₁ inverse steeringmatrix components 324B. Receive signal Y₂ is sent to the Z₁₂, Z₂₂, andZ₃₂ inverse steering matrix components 324B. Receive signal Y₃ is sentto the Z₁₃, Z₂₃, and Z₃₃ inverse steering matrix components 324B.Inverse steering matrix components Z₁₁, Z₁₂, and Z₁₃ send processedreceive signals 325(1), 325(2), and 325(3) to summation block 322(1) forprocessing, which produces transmit signal X₁ 312(1). Inverse steeringmatrix components Z₂₁, Z₂₂, and Z₂₃ send processed receive signals325(4), 325(5), and 325(6) to summation block 322(2) for processing,which produces transmit signal X₂ 312(2). Inverse steering matrixcomponents Z₃₁, Z₃₂, and Z₃₃ send processed receive signals 325(7),325(8), and 325(9) to summation block 322(3) for processing, whichproduces transmit signal X₃ 312(3).

Returning to FIG. 3A, a transmit vector X of transmitted signals 312 isrepresented by X=[X₁, X₂, . . . , X_(n)]^(T) and a receive vector Y ofreceived signals 314 is represented by Y=[Y₁, Y₂, . . . , Y_(n)]^(T). Avariable α is defined as

$\alpha = {e^{i\;\frac{k\;\pi}{n}}.}$Where transmitting elements are adjacent one another k=1, and thisequation reduces to

$\alpha = {e^{i\;\frac{\pi}{n}}.}$If different modulation symbols are transmitted as signals from eachtransmit antenna element 302(1)-302(n), thenY=ΔX,  (3)where

$\Delta = {\begin{bmatrix}1 & \alpha & \ldots & \alpha^{n - 1} \\\alpha & 1 & \ldots & \alpha^{n - 2} \\\vdots & \vdots & \vdots & \vdots \\\alpha^{n - 1} & \alpha^{n - 2} & \ldots & 1\end{bmatrix}.}$Δ represents the steering matrix between transmit array 302 and receivearray 304. Receive analog processor 362 is configured to decode, in theanalog domain, the receive vector Y 314 to recover the transmit vector X312, and thus the transmitted symbols X₁-X_(n). Equation (4), below,represents one exemplary algorithm for recovering the transmit vector X312 from the receive vector Y 314 utilizing the inverse of the steeringmatrix, as follows:X=Δ ⁻¹ Y.  (4)

Thus, when there is line of sight within system 300, transmitted symbolsX₁-X_(n) can be recovered at receive analog processor 362 by applyingthe inverse steering matrix (i.e., Δ⁻¹) to the receive vector Y. Due toprocessing in the analog domain, this method reduces or eliminatesdigitally pre-coding or preprocessing at transmit analog processor 360and digital processing at receive analog processor 362. That is, thereceived signals Y₁-Y_(n) at receive antenna array 304 are processed inthe analog domain by applying the inverse steering matrix Δ⁻¹ to recoverthe originally transmitted signals 312, all prior to any digitalprocessing. For sake of simplicity and clarity, the inverse matrix Δ⁻¹is renamed here as Z, such that,

$\begin{matrix}{Z = {\Delta^{- 1} = {\begin{bmatrix}Z_{11} & Z_{12} & \ldots & Z_{1\; n} \\Z_{21} & Z_{22} & \ldots & Z_{2\; n} \\\vdots & \vdots & \vdots & \vdots \\Z_{n\; 1} & Z_{n\; 2} & \ldots & Z_{nn}\end{bmatrix}.}}} & (5)\end{matrix}$The signal X_(i), which is the ith entry in the transmit vector X, canbe recovered as follows,X _(i)=Σ_(j=1) ^(n) z _(ij) Y _(j).  (6)

It should be understood that the portion of inverse steering matrix Zequation (6) for calculating a transmitted symbol from the set ofreceived signals 314 is represented as the set of Z₁₁-Z_(1n) inversesteering matrix blocks 324, which correspond to the first row of theinverse steering matrix in equation (5). In addition, the summationΣ_(j=1) ^(n), of equation (6) is represented in FIG. 3A as a set of nsummation blocks Σ₁-Σ_(n) 322(1)-(n). FIG. 3A as shown representscalculating the X₁ transmitted signal. It should be understood that anysingle transmitted symbol from the set of transmitted symbols X₁-X_(n)312 or a plurality of transmitted symbols from the set of transmittedsymbols X₁-X_(n) 312 may be calculated.

FIG. 4 illustrates one example of an analog LoS MIMO system, system 400,with a transmit array 402 having two transmit antennas 412(1)-(2) and areceive array 404 having two receive antennas 414(1)-(2), such thatsystem 400 is an n=2 system. Transmit array 402 is connected to transmitanalog processor 460. Receive array 404 is connected to receive analogprocessor 462. Receive analog processor 462 is configured withattenuating splitters 464, phase rotators 466, and summation blocks422(1) and (2). Attenuating splitters 464 and phase rotators 466represented one implementation of an n=2 inverse steering matrix ofequation (5), in an embodiment. It is possible to implement thisdifferently in an n=2 system and may be implemented similarly ordifferently in other, more complex systems, as long as the appropriateinverse steering matrix element Z_(nn) is applied to its correspondingreceive signal.

In operation, transmit analog processor 460 takes as input symbols X₁,X₂ and outputs X₁ to transmit antennas 412(1) and X₂ to transmit antenna412(2) for transmission to receive array 404. Transmit antennas 412(1)and 412(2) transmit symbols X₁ and X₂ as signals 470 and 472,respectively. Receive antenna 414(1) receives signal Y₁ 474 and receiveantenna 414(2) receives signal Y₂ 476. Signal Y₁ 474 is composed ofsignals 470 and 472. As detailed in FIG. 2 and its associateddescription, a separation distance between transmit antennas, in thiscase transmit antennas 412(1) and 412(2), may cause a phase differencebetween two (or more) signals received at a receive antenna in thereceive array. This antenna separation distance based phase differencemay be utilized to facilitate the extraction of the original signals, inthis case X₁ and X₂.

As stated above, system 400 is configured with two transmit 412(1)-(2)and two receive antennas 414(1)-(2), which forms an n=2 system. Based onan n=2 system equation (5) becomes equation (7), below, and the variableα becomes

$\alpha = {e^{\frac{i\;\pi}{2}}.}$With n=2, by applying Euler's formula, and solving the inverse matrix(right hand side of equation (7)), equation (5) becomes the 2 by 2matrix represented on the left hand side of equation (7),

$\begin{matrix}{Z = {\begin{bmatrix}1 & \alpha \\\alpha & 1\end{bmatrix}^{- 1} = {\begin{bmatrix}1 & i \\i & 1\end{bmatrix}^{- 1} = {\begin{bmatrix}0.5 & {{- 0.5}\; i} \\{{- 0.5}\; i} & 0.5\end{bmatrix}.}}}} & (7)\end{matrix}$With i=1 and i=2, equations (6) can be used to extract X₁ and X₂,X ₁=0.5Y ₁−0.5iY ₂  (8)X ₂=−0.5iY ₁+0.5Y ₂  (9)

By way of a second example, with n=3 we get the 3 by 3 matrix,

$\alpha = e^{\frac{i\;\pi}{3}}$With

$\begin{matrix}{Z = {\begin{bmatrix}1 & \alpha & \alpha^{2} \\\alpha & 1 & \alpha \\\alpha^{2} & \alpha & 1\end{bmatrix}^{- 1} = {\begin{bmatrix}\frac{1 - \alpha^{2}}{a^{4} - {2\;\alpha^{2}} + 1} & \frac{\alpha^{3} - \alpha}{\alpha^{4} - {2\alpha^{2}} + 1} & 0 \\\frac{\alpha^{3} - \alpha}{\alpha^{4} - {2\alpha^{2}} + 1} & \frac{1 - \alpha^{4}}{\alpha^{4} - {2\;\alpha^{2}} + 1} & \frac{\alpha^{3} - \alpha}{\alpha^{4} - {2\;\alpha^{2}} + 1} \\0 & \frac{\alpha^{3} - \alpha}{\alpha^{4} - {2\;\alpha^{2}} + 1} & \frac{1 - \alpha^{2}}{\alpha^{4} - {2\;\alpha^{2}} + 1}\end{bmatrix}.}}} & (10)\end{matrix}$and applying Euler's formula, equation (10) becomes,

$\begin{matrix}{Z = {\begin{bmatrix}{0.5 + {0.2887i}} & {{- 5774}i} & 0 \\{{- 0.5774}i} & {0.5 + {0.2887i}} & {{- 5774}i} \\0 & {{- 0.5774}i} & {0.5 + {0.2887i}}\end{bmatrix}.}} & (11)\end{matrix}$Using equation (6) with i=1, 2, and 3 we get X₁, X₂, X₃:X ₁=(0.5+0.2887i)Y ₁+(−5774i)Y ₂  (12)X ₂=(−0.5774i)Y ₁+(0.5+0.2887i)Y ₂+(−0.5774i)Y ₃  (13)X ₃=(−0.5774i)Y ₂+(0.5+0.2887i)Y ₃  (14)

Thus, is can be seen that, in the analog domain, the transmitted symbolsX₁-X_(n) 312 can be recovered from the received symbols Y₁-Y_(n) 314.This greatly reduces processing complexity, time, and power consumption.

FIG. 5 shows one exemplary method 500 for analog LoS MIMO communication.Method 500 is described as being implemented by system 400 of FIG. 4, ann=2 system, although any analog, LoS MIMO system may be use method 500with only minor modifications that are well within the ability of theskilled artisan.

In step 502 method 500 sends transmit symbols to designated antennas ina transmit array. One example of step 502 is transmit analog processor460 of FIG. 4 sending symbol X₁ to antenna 412(1) and symbol X₂ toantenna 412(2).

In step 504 method 500 transmits each symbol for respective antennas assignals. One example of step 504 is antennas 412(1) and 412(2)transmitting symbols X₁ and X₂, respectively.

In step 506 method 500 receives a signal at each antenna in the array ofreceive antennas. One example of step 506 is receive array 404 receivingsignal Y₁ 474 at receive antenna 414(1) and signal Y₂ 476 at antenna414(2).

In step 508 method 500 sends received signals to a connected receiveanalog processor for analog processing. One example of step 508 isantennas 414(1)-(2) (or array 404) sending signals 474-476 to receiveanalog processor 462. Receive analog processor 462 may be implemented asany analog processing unit of collection of analog processing units,either stand alone or incorporated into one or more receive sidecomponent.

In step 510 method 500 applies the inverse steering matrix to thereceived signal. One example of step 510 is receive analog processor 462applying attenuating splitters 464 and phase shifters 466 to receivedsignals Y₁ 474 and received signal Y₂ 476.

In step 512 method 500 extracts the transmitted signal from the inversesteering matrix processed set of received signals. One example of step512 is summation block 422(1) summing signals 478 and 480 and summationblock 422(2) summing signals 482 and 484. In another example of step512, summation block 322(1), FIG. 3A, sums signals received from the setof inverse steering matrix blocks Z₁₁-Z_(1n) 324 resulting in therecovery of transmitted single X₁. The same process occurs for eachinverse steering matrix blocks Z₂₁-Z_(2n)-Z_(n1)-Z_(nm) and associatedsummation block 322(2)-322(n) for the recovery of transmitted signalsX₂-X_(n).

It will be understood after reading the present disclosure that one ormore of, R, λ, and n may be manipulated to optimize the present analog,spatial multiplexing system with LoS propagations to substantiallyoptimize of analog processing. Such an optimization may occur during asetup phase of the present system or may occur periodically.Alternatively, optimization of the present system may be event driven,for example, during or after a weather or environmental event, during orafter disruptive construction or infrastructure work, interference fromone or more other RF source, etc. System optimization may also occurcontinuously or substantially continuously, for example, to compensatefor persistent fluctuation that affect system utilized phase delays. Anyone of these optimization process may utilize known techniques, onenon-limiting example of which is a receiver-to-transmitter feedback loopfor mechanically, arithmetically, or otherwise adjusting one or more ofR, λ, n, the steering matrix, the inverse steering matrix, etc.

One manner in which optimization may occur is by adjusting thearray-to-array distance R such that a transmitted signal arrives at areceive element out of phase by a desired amount. Although notnecessary, such manipulations need only be within the range of less thana wave length. Alternatively, another optimization technique isadjusting the wavelength of the transmit signal, again with the aim ofoptimizing when the transmitted signal arrives at a receive element suchthat the phase delay is optimized to facilitate analog processing.Optimization may also be performed by adjusting the minimum distancebetween array elements. Adjusting the minimum distance between arrayelements may be accomplished in multiple ways, one non-limiting exampleof which is pruning elements, such as eliminating every other transmitelement from a cycle of transmissions. This process will also reduce thenumber of elements active in a communication step. Pruning may also beused to reconfigure the elements of an array, for example, in thesituation where a broken or otherwise inoperable array element exists.The inter-element distance may also be adjusted in other was, includingbut not limited to mechanically adjusting the distance between arrayelements.

The present system and method is disclosed herein as being configuredwith transmit and receive arrays having a parallel and opposingorientation such that the shortest distance between a transmit elementand a receive element is the array to array separation distance R. Inreality, this idealized situation may not even be achievable.Adjustments to the system may be made to compensate for non-idealorientation. In one embodiment, orientation adjustments are performedmechanically. In another or the same embodiment, orientation adjustmentsare performed arithmetically. Arithmetically manipulations may beapplied on an element by element basis such as by “virtually” adjustingone or more of R, λ, and n by adding or subtracting a constant orapplying a situation based function to one or more of the parameters.Alternatively, orientation compensating arithmetic manipulations may beapplied to the steering matrix, the inverse steering matrix, included asa static or dynamically adjusted variable, etc. Such manipulations arewell within capability of the skilled artisan after reading the presentdisclosure.

It will also be understood that the separation distance D betweentransmit elements in the transmit array need not be the same as theseparation distance between the receive element in the receive array.The present disclosure and associated figures show symmetry betweentransmit and receive arrays, but this is merely to simplify the drawingsand associated description and is not meant to be limiting in any way.If changes are made to the separations distance in one or both of thetransmit array and the receive array, the above equations may bemodified accordingly, but such modifications are well within thecapabilities of one skilled in the art after reading the presentdisclosure.

It will also be understood that the separation distance D betweenelements is the minimum separation distance. Other separation distancethat satisfy the phase delay requirements for facilitating analogprocessing as detailed above may be used without departing from thescope herein.

Changes may be made in the above methods and systems without departingfrom the scope hereof. It should thus be noted that the matter containedin the above description or shown in the accompanying drawings should beinterpreted as illustrative and not in a limiting sense. The followingclaims are intended to cover all generic and specific features describedherein, as well as all statements of the scope of the present method andsystem, which, as a matter of language, might be said to fall therebetween.

What is claimed is:
 1. An analog, line of sight (LoS) spatialmultiplexing system, comprising: a transmit analog processor; a transmitarray configured with a first transmit element and a second transmitelement spaced apart by no less than a distance D, the first transmitelement in communication with the transmit analog processor forreceiving a first modulation symbol for transmitting as a first transmitsignal, the second transmit element in communication with the transmitanalog processor for receiving a second modulation symbol fortransmitting as a second transmit signal; a receive array configuredwith a first and a second receive element, the first receive elementconfigured to receive a first receive signal comprising a combination ofat least the first and the second transmit signals, the second receiveelement configured to receive a second receive signal comprising adifferent combination of at least the first and second transmit signals;and a receive analog processor in communication with the receive arrayfor processing the first and second receive signals in the analog domainto recover at least one of the first transmit signal and the secondtransmit signal.
 2. The system of claim 1, wherein the first modulationsymbol is different from the second modulation symbol.
 3. The system ofclaim 1, wherein R is a distance between the first transmit element andthe first receive element, λ is a transmit wavelength of at least thefirst transmit signal and one or more of D, R, and λ relates to a phasedelay between the first and second transmit signals and are adjustableto optimize the phase delay.
 4. The system of claim 1, wherein R is adistance between the first transmit element and the first receiveelement, n is the number of antenna elements in one or both of thetransmit and receive arrays, and λ is a transmit wavelength of the firstand second transmit signals such that the distance between the secondtransmit element and the first receive element is$\sqrt{D^{2} + R^{2}} = {\sqrt{\frac{R\;\lambda}{n} + R^{2}} = {{{R\sqrt{1 + \frac{\lambda}{n\; R}}} \approx {R\left( {1 + \frac{\lambda}{2\; n\; R}} \right)}} = {R + {\frac{\lambda}{2n}.}}}}$5. The system of claim 4, further comprising a k^(th) transmit element,wherein the distance between the k^(th) transmit element and the firstreceive element is $R + {\frac{k\;\lambda}{2\; n}.}$
 6. The system ofclaim 4, wherein n is the number of transmit antenna elements in thetransmit array, and a steering matrix between transmit array and receivearray is ${\Delta = \begin{bmatrix}1 & \alpha & \ldots & \alpha^{n - 1} \\\alpha & 1 & \ldots & \alpha^{n - 2} \\\vdots & \vdots & \vdots & \vdots \\\alpha^{n - 1} & \alpha^{n - 2} & \ldots & 1\end{bmatrix}},{\alpha = e^{\frac{i\;\pi}{n}}},$ an inverse steeringmatrix is ${Z = {\Delta^{- 1} = \begin{bmatrix}Z_{11} & Z_{12} & \ldots & Z_{1\; n} \\Z_{2\; 1} & Z_{22} & \ldots & Z_{2\; n} \\\vdots & \vdots & \vdots & \vdots \\Z_{n\; 1} & Z_{n\; 2} & \ldots & Z_{nn}\end{bmatrix}}},$ and a formula for recovering an i^(th) transmitsignal, X_(i), isX _(i)=Σ_(j=1) ^(n) z _(ij) Y _(j).
 7. The system of claim 6, wherein ani^(th) modulation symbol can be recovered from the i^(th) recoveredtransmit signal X_(i).
 8. The system of claim 1, wherein the number andarrangement of transmit antenna elements and/or receive antenna elementsmay be adjusted to optimize one or both of the distance D and thedistance R.
 9. The system of claim 1, wherein an inverse steering matrixis utilized to recover the transmitted data.
 10. The system of claim 9,wherein the inverse steering matrix is based at least in part on a fixedarray-to-array distance.
 11. The system of claim 9, wherein the inversesteering matrix is based at least in part on a known array-to-arraydistance.
 12. The system of claim 11, wherein the known array-to-arraydistance is manipulated to compensate for non-ideal opposingorientations.
 13. The system of claim 12, wherein manipulating the knownarray-to-array distance is accomplished by mechanical adjustments to theorientation of one or both of the arrays.
 14. The system of claim 12,wherein manipulating the known array-to-array distance is accomplishedon an element by element basis such as by adjusting one or more of R, λ,D, and n by adding or subtracting a constant.
 15. The system of claim12, wherein manipulating the known array-to-array distance isaccomplished by applying a situation based function to one or moreparameters R, λ, and D.
 16. The system of claim 12, wherein orientationcompensation is an arithmetic manipulation of one of the steering matrixand the inverse steering matrix.
 17. The system of claim 12, wherein thearithmetic orientation compensation includes a static operationcomprising applying a constant to one of the steering matrix and theinverse steering matrix.
 18. The system of claim 12, wherein arithmeticorientation compensation includes a dynamic operation comprising theapplication of a dynamically adjusted variable to one of the steeringmatrix and the inverse steering matrix.
 19. The system of claim 1, wherethe one or both of the transmit array and the receive array are uniformlinear array.
 20. The system of claim 1, where the one or both of thetransmit array and the receive array are uniform planar array.